Critical Path Analysis: Network Diagrams and the Critical Path
Critical path analysis (CPA) is a project-planning technique that models a project as a network diagram of activities, each shown on an arrow (or node) with its duration, connected in the order they must be completed. Each activity node shows its earliest start time (EST), calculated with a forward pass through the network (the earliest an activity can begin, given all the activities before it), and its latest finish time (LFT), calculated with a backward pass from the end of the project (the latest an activity can finish without delaying the whole project). The critical path is the longest route through the network from start to finish, and it determines the minimum possible duration of the whole project; every activity on the critical path has zero float, meaning it cannot be delayed at all without delaying the entire project. Float is the amount of spare time an activity that is not on the critical path has: how long it could be delayed, or take longer than planned, without pushing back the whole project.
Before you start
Make sure you're comfortable with these topics first:
Method
- List every activity, its duration, and which activities must be completed immediately before it can start.
- Draw or read the network diagram and carry out a forward pass: for each activity, its EST equals the EST of the activity before it plus that activity's duration (or the highest such value, if more than one activity feeds into it).
- Carry out a backward pass from the final activity's finish time: for each activity, its LFT equals the LFT of the activity after it minus that following activity's duration (or the lowest such value, if the activity feeds into more than one following activity).
- Calculate the float of any activity not obviously on the critical path: float = LFT - EST - duration (or, equivalently, LST - EST, where LST is the latest start time).
- Identify the critical path as the sequence of activities with zero float running from the start to the end of the network; its total duration is the minimum time the whole project can take.
- For a business question, explain the practical implication: activities on the critical path must be closely monitored and given priority resources, since any delay to them delays the whole project, while activities with float offer some scheduling flexibility.
Worked example
A project has five activities: A (4 days, no predecessor), B (3 days, after A), C (6 days, after A), D (5 days, after B), and E (2 days, after both C and D). Identify the critical path and the minimum project duration, and calculate the total float on activity C.
- Forward pass: A starts at 0, finishes at 0 + 4 = 4. B starts when A finishes, at 4, finishes at 4 + 3 = 7. C starts when A finishes, at 4, finishes at 4 + 6 = 10. D starts when B finishes, at 7, finishes at 7 + 5 = 12.
- E depends on both C and D, so it can only start once both are finished: E starts at the later of the two, max(10, 12) = 12, and finishes at 12 + 2 = 14.
- The project's minimum duration is 14 days, set by the finish time of the final activity, E.
- Backward pass: E's latest finish time is 14 (the project end), so E's latest start time is 14 - 2 = 12. Both C and D must finish by E's latest start time of 12, so C's latest finish time is 12 and D's latest finish time is 12.
- C's latest start time = 12 - 6 = 6. C's earliest start time (from the forward pass) is 4.
- Float on C = latest start time - earliest start time = 6 - 4 = 2 days, meaning C could start up to 2 days later than its earliest possible start without delaying the whole project. Checking path A-C-E (4 + 6 + 2 = 12 days) against the critical path A-B-D-E (4 + 3 + 5 + 2 = 14 days) confirms the 2-day gap.
- Since B, D and E all have zero float (calculated the same way), the critical path is A-B-D-E, with a total duration of 14 days.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1What does EST stand for in critical path analysis?Show answer
Answer: Earliest start time.
Q2What does the critical path represent in a network diagram?Show answer
Answer: The longest route through the network from start to finish, which sets the minimum possible duration of the whole project.
Q3State the float of any activity that lies on the critical path.Show answer
Answer: Zero.
Q4An activity has an earliest start time of 6 days and a latest start time of 9 days. Calculate its float.Show answer
Answer: Float = latest start time - earliest start time = 9 - 6 = 3 days.
Q5Give one benefit to a business of using critical path analysis before starting a large project.Show answer
Answer: It identifies the minimum time the project will take and which activities must not be delayed, allowing managers to prioritise resources and monitoring on the critical activities.
Q6Explain why delaying a non-critical activity by less than its float does not delay the whole project.Show answer
Answer: Because float is defined as the spare time an activity has before it starts affecting the following activities' start times, so as long as the delay stays within that spare time, the project's overall finish date is unaffected.
Exam-style questions
Written in the style of a A Level Business exam paper, with a full mark scheme.
Analyse the benefits to a business of using critical path analysis when planning a new project.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 9 available
SolarBuild is planning to install a solar panel system for a client. The project has four activities: Survey the roof (2 days, no predecessor), Order panels (5 days, after the survey), Install scaffolding (3 days, after the survey), and Fit panels (4 days, after both the panel order and the scaffolding are complete). SolarBuild has promised the client the system will be finished within 12 working days. Using critical path analysis, evaluate whether SolarBuild can meet this deadline.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 16 available
See real A Level Business past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the critical path analysis: network diagrams and the critical path worksheet pack - 5 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
Next topics
Not quite what you needed?
Tell us what is missing on critical path analysis: network diagrams and the critical path, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.